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A note on triangulations of sumsets
In R2, for finite sets A and B, we write A+B = {a+ b : a ∈ A, b ∈ B}. We write tr(A) to denote the common number of triangles in any triangulation of the convex hull of A using the points of A asExpand
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Poisson Structures and Potentials
We introduce the notion of weakly log-canonical Poisson structures on positive varieties with potentials. Such a Poisson structure is log-canonical up to terms dominated by the potential. To aExpand
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Stacky Hamiltonian actions and symplectic reduction
We introduce the notion of a Hamiltonian action of an \'etale Lie group stack on an \'etale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-WeinsteinExpand
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A note on triangulations of sum sets
For finite sets A and B in the plane, we write A+B to denote the set of sums of the elements of A and B. In addition, we write tr(A) to denote the common number of triangles in any triangulation ofExpand
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Iterated functions and the Cantor set in one dimension
In this paper we consider the long-term behavior of points in ${\mathbb R}$ under iterations of continuous functions. We show that, given any Cantor set $\Lambda^*$ embedded in ${\mathbb R}$, thereExpand
Toric Symplectic Stacks.
We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This generalizes Delzant'sExpand
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Canonical bases and collective integrable systems
Let K be a non-abelian compact connected Liegroup. We show that every Hamiltonian K-manifold M admits a Hamiltonian torus action of the same complexity on a connected open dense subset. The momentExpand
Concentration of symplectic volumes on Poisson homogeneous spaces
For a compact Poisson-Lie group $K$, the homogeneous space $K/T$ carries a family of symplectic forms $\omega_\xi^s$, where $\xi \in \mathfrak{t}^*_+$ is in the positive Weyl chamber and $s \inExpand
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Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization
Let $G$ be a connected semisimple Lie group. There are two natural duality constructions that assign to it the Langlands dual group $G^\vee$ and the Poisson-Lie dual group $G^*$. The main result ofExpand
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Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization
Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variables on these spacesExpand
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